We are probably going to add something like WebDocument.ParentForm
which you can .Minimize()/.Maximize().

Close() should rather close the tab it is in rather then the whole browser.

But it should be no problem to add a ShowFullScreen = true|false.

As workaround for fullscreen, you have to send "{F11}" which has the same effect. To check if IE is already in fullscreen mode you can compare the height of the WebDocument DOM with the Internet Explorer Form height (or screen height) which is the same if the status bar is switched off.